Baseband time-domain communications method

ABSTRACT

A communications system reduces downconverter inaccuracies in time-domain measurements or samples of received microwave communications I and Q complex signals by converting received signal to baseband taking measurements or samples of the I and Q waveforms at differing phase shifts of a demodulating carrier signal for a local oscillator or carrier tracking loop used during downconversion so that I and Q imbalances may be detected and removed by lowpass equivalent averaging for improved characterization of downconverters or for improved signal reception. In the preferred form, the phase shifts are 0 and π/2 for a conventional measurement, and then at θ, and θ+π/2, with θ=π/4+mπ/2 for an integer m for the second measurement where I and Q imbalances and baseband nonlinearities are indicated by differences between the two measured or sampled signals, where θ provides for optimum error detection for reducing the errors by averaging the measurements.

REFERENCE TO RELATED APPLICATION

This application is a continuation of Ser. No. 10/860,232, now U.S. Pat.No. 7,321,641, filed Jun. 3, 2004, having common inventors.

FIELD OF THE INVENTION

The invention relates to the field of measurement methods of electronicsignals and devices. More particularly, the invention relates tobaseband time-domain measurement methods of communications signals, suchas modulated waveforms used in communication systems. Further still, theinvention relates to methods for measuring the performancecharacteristics of nonlinear and linear devices used in communicationssystems such as power amplifiers used in transmitters. The inventionfurther relates to receiver systems generating balanced basebandreceived signals for reducing imbalances in downconverters for improvedsignal reception.

BACKGROUND OF THE INVENTION

Modulated microwave signals are used to carry information in a widevariety of electronic communications systems. Examples include modulatedmicrowave signals used to transmit voice and data or video signals froma ground transmitter through space to a satellite, and then back fromthe satellite to a ground receiver. Another example is a televisiontransmitter, which transmits modulated signals that carry the pictureand sound to television sets. Another example is a cellular basestation, which transmits modulated microwave signals that carry thevoice information to cellular phones. Such signals must be accuratelymeasured for conformance to systems specifications and for accuratemodeling of deviations from ideal performance.

It is also desirable to use such modulated microwave signals tocharacterize nonlinear devices, such as power amplifiers, used incommunications systems, because these are the signals that the devicesreceive in operation. Nonlinear electronic devices are the mostdifficult elements to model accurately in communications simulations. Arecent example is the design and simulation of power amplifiers for usein digital cellular applications. In this case, the transmit poweramplifier must be operated at or near saturation for high efficiency,and still meet stringent adjacent channel power requirements. This is anexample where accurate, computationally efficient nonlinear models arerequired to make the proper design tradeoffs. Also known as black-boxmodels, these models are computationally efficient because theytransform an input waveform to the correct output waveform withoutresorting to the details of circuit operation. These models seek tocharacterize the nonlinear amplifier through the use of a selected setof probing signals. The degree of predictive fidelity of thesesimulation models must be checked with the class of operational signalsexpected, such as modulated microwave signals.

Accurate measurement of communication signals in the time domain may beused to construct and validate high fidelity communications system andcomponent models. This is a significant advance over the traditionaltechnique of basing such models on single-tone vector-network-analyzermeasurements of the component or system. Unlike single-tonemeasurements, time-domain waveforms contain all the informationnecessary to accurately characterize the component or system over thebandwidth of the waveforms. In particular, nonlinear interactionsbetween different frequency components of a communications signal arecaptured in a time-domain measurement of the waveform, but ignored in atraditional single-tone frequency measurement. Time-domain waveformmeasurements may be used to characterize nonlinear components such aspower amplifiers. An outline of the procedure follows. A waveform sourcehaving the same modulation type as that intended for the application maybe used as the test signal to be applied to the amplifier. Time-domaininput and output measurements of these test signal waveforms capture theresponse of the power amplifier to the class of signals that are appliedto it. In contrast, single-tone measurements cannot capture thenonlinear dynamic response of the amplifier to input signals havingnon-negligible bandwidth. A nonlinear model constructed from time-domainwaveform measurements is accurate over wiser bandwidths than modelsconstructed from traditional single-tone input-output measurements.

The time-domain measurement of microwave communications signals isconveniently performed by first converting the microwave signal tobaseband. This procedure yields inphase (I) and quadrature (Q)waveforms. The I and Q baseband waveform is commonly expressed incomplex notation and is termed the lowpass equivalent (LPE) signal inthe context of simulations. The accuracy of the measured waveform islimited by distortions introduced by the waveform measurement process.These distortions fall into four categories including linear filterdistortions in the downconverting receiver, I and Q amplitude and phaseimbalance, baseband nonlinearities such as amplifier compression and A/Dnon-ideality, and RF nonlinearities such as mixer compression. It isdesirable to minimize the distortions. Limiting the input signal levelto the downconverting receiver minimizes distortions due to baseband orRF nonlinearities. Linear filter distortions may be removed by afrequency-response calibration of the downconverter. The phase andamplitude response of the downconverting receiver cannot be measureddirectly by a vector network analyzer because the receiver input andoutput frequencies are different. The calibration procedure is used toextract the frequency response of the downconverting receiver by makingthree pair-wise measurements of two additional frequency converters andthe downconverting receiver. One of the additional frequency convertersmust have a reciprocal frequency response, that is, the response must bethe same whether it is used as an upconverter or a downconverter. Thisassumption of reciprocity is accurate enough to reduce linear filterdistortions in the downconverting receiver to a low level overmulti-Gigahertz bandwidths.

A prior procedure of measurement of modulated microwave signals is torecord directly the radio frequency (RF) or microwave signal by means ofa digital storage oscilloscope or other waveform recorder. Formeasurement of nonlinear devices, the RF or microwave frequencywaveforms must be measured at the input and output of the device to findthe input-to-output characteristic. These waveforms should be recordedat a number of input power levels throughout the operating range of thenonlinear device. Examples of such nonlinear components are asolid-state power amplifier or a traveling-wave tube amplifier.Time-domain instrumentation can record the waveform data digitally andstore the data directly on a controlling computer.

Typical instruments used for recording waveform data are a digitalstorage oscilloscope (DSO), a microwave transition analyzer (MTA), or arecently developed large signal network anlayzer (LSNA). The accuracy ofthese instruments for measuring high-frequency signals is limited bylinear amplitude and phase distortion. The MTA and high bandwidth DSOhave significant phase and amplitude distortion beginning at frequenciesabout about 15.0 GHz. The LSNA is based on an MTA, but the LSNA comeswith calibration standards and an extensive calibration routine so thatphase and amplitude distortion, and other errors, are analyticallyremoved from the measurements. The LSNA performs calibrated time-domainmeasurements of signals up to 50.0 GHz. This LSNA includes calibrationstandards and software that calibrates the sampling oscilloscope foranalog and digital nonlinearity, and gain and phase responses over afrequency range. Hence, the LSNA can provide accurate waveforms up to50.0 GHz. The LSNA calibration eliminates any inaccuracy associated withthe gain and phase response of the sampling oscilloscope, however, theLSNA still has limitations imposed by a limited number of samples andphase noise errors. The LSNA is an advanced and expensive system,however, and requires a specialized calibration procedure. Additionally,the LSNA can only be used to characterize arbitrary waveforms of alimited bandwidth.

Another prior waveform measurement approach is to use an uncalibrateddownconverter with separate I and Q output signals. These I and Q outputsignals are then recorded by means of a DSO. This technique also yieldsthe time-domain baseband waveform, but is corrupted by the linear filterdistortions, and nonlinear baseband distortion, nonlinear RFdistortions, and the I and Q imbalance between the I and Q signals inthe downconverter. The unknown distortions can be large enough toseverely limit the utility of the waveform data for a precisionapplication such as communications system modeling.

A recent measurement approach measures the transmission response of afrequency-translating device (FTD), such as a mixer. The response of theFTD, including a downconverter, may be measured by means of thebaseband-double-sideband-mixer FTD characterization method, as describedin the related patent. In this FTD characterization method, threepair-wise combinations of an upconverter referred to herein as atransmitter, a test mixer, and the donwconverter referred to herein as areceiver, are measured. The transmission response of the downconvertingreceiver is then calculated from these measurements. The testconfiguration setup for this FTD characterization method consists ofconnecting an upconverting transmitter FTD to a downconverting receiverFTD with both using the same local oscillator (LO) but with a phaseshifter in the downconverter LO path. A vector network analyzer (VNA) isused to measure this first paired combination at two relative LO phasesettings 90° apart. The additional test mixer is used in the second ofthese measurements as a downconverter. The FTD characterization methodrequires that the test mixer have the same frequency response, which isa reciprocal frequency response, whether the test mixer is used as anupconverter or a downconverter. In practice, commonly availabledouble-balanced mixers exhibit this reciprocal response if a low voltagestanding wave ratio (VSWR) is provided on all ports by use of fixedattenuators. These six measurements, for the three configurations withzero and with ninety degree phase shift, are sufficient to extract thefrequency response of all three FTDs, including the downconvertingreceiver. By mathematically combining the six measurements provided bythe three-setup configuration, with and without the 90° phase shift, thelowpass equivalent (LPE) frequency response of the downconvertingreceiver may be obtained.

In U.S. Pat. No. 6,211,663 entitled Baseband Time-Domain WaveformMeasurement Method, issued Apr. 3, 2001, a time-domain basebandmeasurement method measures modulated microwave signals typically usedin communication systems by converting microwave signals to basebandbefore measurement for improved accuracy compared to direct measurementat the microwave frequency. A downconverting receiver is firstcharacterized using a prior characterization method and then themodulated microwave signal is applied to the downconverting receiver andthe response of the downconverting receiver is removed to provide anaccurate characterization of the modulated microwave signal. Such anaccurate measurement of the modulated microwave signal can be used forcommunications system performance verification as well as forcharacterizing communications devices and systems. One particularapplication is the measurement of input/output characteristics ofnonlinear power amplifiers using such modulated microwave signals. Sucha system produces imbalances of the I and Q signals upon carrierdemodulation. The method includes inserting local oscillator phaseshifts for measuring downconverter DC offsets. However, the method doesnot remove all I and Q imbalances that lead to distortion of the inputsignal during downconversion. These and other disadvantages are solvedor reduced using the invention.

SUMMARY OF THE INVENTION

An object of the invention is to provide a system for measuringimbalances in downconverters.

Another object of the invention is to provide a system for providinglowpass equivalent of received signals.

Yet another object of the invention is to provide a system fordetermining lowpass equivalencies of received signals by removingdownconverter imbalances.

Still another object of the invention is to provide a system forproviding baseband lowpass equivalencies of received signal by removingdownconverter imbalances using selected phase shift of a demodulatingcarrier signal.

A further object of the invention is to provide a system for providingbaseband lowpass equivalencies of received signal by removingdownconverter imbalances using selected phase shift of a demodulatingcarrier signal using 0 and π/2 phase shifts for providing a firstbaseband lowpass equivalence of received I and Q complex signals andusing θ and θ+π/2 phase shifts for providing a second baseband lowpassequivalence of the received I and Q complex signals.

Yet a further object of the invention is to provide a system forproviding baseband lowpass equivalencies of received signal by removingdownconverter imbalances using selected phase shift of a demodulatingcarrier signal using 0 and π/2 phase shifts for providing a firstbaseband lowpass equivalence of received I an Q complex signals andusing θ and θ+π/2 phase shifts for providing a second baseband lowpassequivalence of the received I and Q complex signals with θ=π/4+mπ/2where m is an integer.

The present invention is directed towards a system for minimizinginaccuracies in time-domain measurements of microwave communicationssignals and for removing the effects of downconverter imbalances incommunication receivers. The signal measurements are accomplished byconverting the signal to baseband where accurate instrumentation isavailable. The baseband signal is a complex signal composed of I and Qcomponents. The I and Q waveform measurements differ by π/2 phase shiftsof a carrier signal provided by a local oscillator (LO) or carriertracking loop used in the downconversion. Any I and Q imbalances may bedetected and reduced by requiring the complex baseband signal to beinvariant and apart from a rotation in the complex plane thatcorresponds to a change in the local oscillator phase. The complexbaseband signal is measured or sampled twice, where the LO phase shiftis 0, and π/2 for the first signal measurement or sampling, and θ, andθ+π/2 for the second. Any I and Q imbalances and baseband nonlinearitiesare indicated by differences between the two measured or sampledsignals. The LO phase shift of θ=π/4+mπ/2, where m is an integer, isoptimum or error detection and imbalance correction of the generatedlowpass equivalencies of the measured or sampled signal. The imbalanceerrors may be reduced by averaging the measurements and by optimizationof the measurement system. Errors caused by I and Q imbalances have beenreduced to an error-to-signal power ratio of less than −56 dB. Thisaccuracy is sufficient for communications system modeling applications.

For waveform measurements, the invention reduced I and Q imbalances as afunction of frequency because the same downconverting receiver is usedfor both waveforms. However, an overall phase imbalance may be caused byerrors in the phase shifts. Similarly, an overall amplitude imbalancemay be caused by LO power level changes between the measurement of the Iand Q components. Measurement errors or imbalances caused by I and Qimbalances and baseband nonlinearities are quantifiable and hence, canbe removed. The communication system can be adapted to minimizeimbalance errors to enhance the usefulness of baseband waveformmeasurements and receivers. These and other advantages will become moreapparent from the following detailed description of the preferredembodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of a baseband time-domain test configuration.

FIG. 2 is a block diagram of a baseband time-domain transmitter.

FIG. 3 is a block diagram of a baseband time-domain receiver.

FIG. 4 is a block diagram of a balanced baseband receiver system.

FIG. 5 is a graph of a signal vector plot in an I-Q complex coordinatesystem.

FIG. 6 is a graph of an ideal and distorted QPSK constellation plot.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

An embodiment of the invention is described with reference to thefigures using reference designations as shown in the figures. Referringto FIGS. 1, 2 and 3, the baseband time-domain basic measurement testconfiguration system consists of an upconverting transmitter 10 and adownconverting receiver 12, both driven by a local oscillator generator14, for measuring baseband waveforms. The oscillator generator 14includes a local oscillator (LO) 16, a splitter 18 providing a localoscillator signal to an isolator 20 and phase shifter 22. The isolator20 provides a fixed phase local oscillator signal 24 that may beconsidered as a carrier signal. The phase shifter 22 provides a variablephase local oscillator signal 25 that is used for coherentdownconversion. In a broad form, the preferred transmitter 10 is drivenby a baseband signal source 26 for providing a baseband test signal tothe transmitter 10 and for providing a 10 MHz reference signal 27 and atrigger signal 59. The transmitter 10 includes a mixer 28, microwaveamplifier 30 and attenuator 32. The baseband signal source 26 providesthe baseband test signal that drives the upconverter 28 receiving thefixed phase LO signal 24 for providing an unconverted signal to themicrowave amplifier 30 that in turn drives the attenuator 32 providing amicrowave test signal 34. When testing a device under test (DUT) 36, themicrowave test signal is applied directly to the DUT 36 providing amicrowave response signal 38. When characterizing an arbitrary microwavetest signal, such as the microwave test signal 34, the microwave testsignal 34 becomes a microwave test signal 38 applied directly to thereceiver 12. Hence, the transmitter 10 can be any arbitrary systemproviding an arbitrary repetitive modulated microwave test signal 34. Inthe broad form of the invention, the microwave test signal 34 is themicrowave test signal 38 connected directly to the receiver 12 forcharacterization of the microwave test signal 34 and 38 withoutcharacterizing the DUT 36 with the DUT 36 effectively removed as a shortcircuit having no responsive characteristics.

In preferred form, the DUT 36 is inserted between the transmitter 10 andreceiver 12. The receiver 12 includes a downconverter 40 and a basebandamplifier 42. When excited by the microwave test signal 34, the insertedDUT 36 provides a microwave response signal 38 to a downconverter 40that also receives the variable phase LO signal 25 and provides adownconverted signal to the baseband amplifier 42 that in turn providesa baseband response signal that is recorded by an analyzer 44. Themicrowave signals 34 and 38 of the DUT to be measured can have anyarbitrary repetitive phase or amplitude modulation, but the microwavesignals 34 and 38 must be accompanied by unmodulated LO signals 24 and25 to respective upconverter 28 and downconverter 40 of transmitter 10and receiver 12, respectively. The trigger signal 59 must also besupplied to analyzer 44, while the reference signal 27 is optional. Thetransmitter 10 and receiver 12 operate respectively using the fixedphase LO signal 24 and the variable phase LO signal 25, which arecoherent LO signals. These coherent LO signals 24 and 25 are used duringtesting and calibration procedures. The analyzer 44 is preferably amicrowave transition anlayzer (MTA), but could also be a digital storageoscilloscope (DSO) used in place of the MTA with reduced accuracy,because most DSOs do not have the calibrated accuracy of an MTA. Thetransmitter 10 may further include an isolator 50 connected between themicrowave amplifier 30 and attenuator 32. The downconverting receiver 12may further include bias tee coupler 54 for providing a voltage signalto a voltmeter 56. A power meter 57 is used to measure the power of themicrowave test signal, from the transmitter 10, or the microwaveresponse signal 38 when the DUT 36 is inserted. The receiver 12 mayfurther include attenuators 58 and 60 for impedance matching. The DClevel of the downconverted signal from the downconverter 40 is separatedfrom the LPE signal by the bias tee 54 and corresponds to the Fouriercomponent at the LO frequency. The DC level that is separated by thebias tee 54 is measured by the volt meter 56 at the output of thedownconverter 40 that may also be a mixer. The measurement of the DClevel is preferred because the baseband amplifier 42 blocks the DCcomponent of the baseband response signal from the downconverter 40. Thefrequency stability requirements on the local oscillator signals 24 and25 from oscillator 16 need not be high because the phase noise iscanceled by downconversion in the receiver 12. The baseband modulationsignal provided to the upconverter 28, which is a mixer 28, however,must be stable, preferably with a 10.0 MHz reference output 27 to beused by the MTA 44 as an external reference. The modulating basebandsource 26 must also be used to trigger the MTA 44 using trigger signal59.

The transmitter 10 provides the microwave test signal 34 to the DUT 36or to the receiver 12 to produce the baseband LPE waveform that isrecorded by the MTA 44. At the same time, the DC component at the phaseshifter setting is recorded, scaled to take into account the gain of thebaseband amplifier 42, and added to the baseband LPE waveform. The phaseshifter 22 is then adjusted by 90° and the downconverted baseband signaland the corresponding DC component are again recorded and combined toyield the uncorrected quadrature component of the LPE signal. Enhancedmeasurement accuracy of the Fourier component at DC is provided byperforming a zeroing procedure consisting of another DC measurement atboth phase settings with no microwave test signal input and subtractingthe DC values thus obtained from the measurements with the microwavetest signal applied. This zeroing procedure may be applied periodicallyto eliminate drift. If the ultimate DC component accuracy is required,measurements at four phase settings are used to provide enhancedcancellation of DC mixer offsets. The 0° and 135° measurements arecombined to form the inphase component, and the 90° and the inverse ofthe 225° measurements are combined to form the quadrature component.This procedure eliminates any drift that can occur during the timeinterval between the DC zeroing procedure and the time at which thebaseband waveform data is recorded. Because the same downconvertingreceiver 12 is used to measure both the I and the Q waveforms, there isno I/Q imbalance. The LPE signals thus obtained include the frequencyresponse of the receiver 12 and are therefore uncorrected. To obtaincorrected LPE signals, the frequency response of the receiver 12 must beremoved. The response of the receiver 12 is removed analytically fromthe uncorrected signals by means of the prior baseband-double-sidebandfrequency translating device FTD characterization method. The receiverresponse may then be removed analytically from the uncorrected LPEsignal measurements, leaving an accurate LPE representation of themicrowave test signal.

Referring to FIGS. 4, 5 and 6, the test method can be implemented in areceiver system that eliminates downconverter imbalances for improvedperformance using modulated signals 61. The function of signalmodulation is to carry information from a transmitter to the receiver,typically in quadrature. The modulation format may be anyamplitude-phase-shift-keyed modulation, such asquadrature-phase-shift-keying (QPSK) having four or more distinctamplitude and phase states such as those shown in FIG. 6. The functionof the receiver is to convert and process the received signal 61. Thebalanced baseband receiver system receives the modulated signal 61 atthe input at the defined carrier frequency using carrier modulation. Themodulated signal 61 is fed into a carrier-tracing loop 62 for extractingthe carrier, as is conventional practice. The carrier signal is thensplit by splitters 63, 64, and 66 for providing four carrier replicasthat are respectively fed into a 0° phase shifter 68, a 90° phaseshifter 70, a 135° phase shifter 72, and a 225° phase shifter 74. The0°, 90°, 135°, and 225° phase shifted carrier replicas are respectivelyfed to downconverters 76 a, 76 b, 76 c, and 76 d. The input signal 61 isalso split four ways using splitters 80, 82 a, and 82 b for generatingfour input signal replicas. Each input signal replica from the splitter80, 82 a, and 82 b, is downconverted by the downconverters 76 a, 76 b,76 c, and 76 d, which form two I and Q pairs. The function of the firstpair of downconverters 76 a and 76 b is to remove the carrier relativeto two particular phases of the carrier at 0° and 90°. The two basebandoutputs of the first I and Q converters 76 a and 76 b are independentcarrier demodulated signals which have an orthogonal phase relationshipto each other.

The function of the second pair of downconverters 76 c and 76 d toremove the carrier relative to two particular phases of the carrier at135° and 225°. The two baseband outputs of the second I and Q converters76 c and 76 d also provide independent carrier demodulated signals,which also have an orthogonal phase relationship to each other.

The output of the first pair of I and Q downconverters 76 a and 76 b,and the output of the second pair of I and Q downconverters 76 c and 76d are ideally identical to each other within a rotation of 135° in thecomplex plane. However, when the enhanced receiver is implemented inhardware, there are several factors that make the outputs of the twoconverters less than perfect, even after precise rotation in the complexplane of 135° of the output of the first downconverter pair. First, theamplitude and phase responses of the downconverters are never perfectlyidentical. Second, the phase shifters that define the phase shiftapplied to the carrier input of each of the downconverters are neverperfectly realized. Third, the power splitters 68, 70, 72, and 74 thatare used to split the signals also introduce phase and amplitude errors.Hence, signal processing is required to remove these errors, using asampling clock signal from a clock recovery loop 83. The low-passfilters (LPF) remove the unwanted upper sidebands and out-of-band noisepresent at the outputs of each of the four mixers. The filtered outputsof the mixers are then applied to the inputs of four analog-to-digital(A/D) converters to convert the analog outputs of the downconvertingmixers 76 a, 76 b, 76 c, and 76 d to a binary representation of a numberproportional to the instantaneous signal amplitude. The instantaneoussignal amplitude at the input to the A/D converter is sampledsynchronously at the transmitted data rate when triggered by therecovered data clock from the clock recovery loop 83. The downconvertedsignals from the downconverting mixers 76 a, 76 b, 76 c, and 76 d, arefirst passed through respective lowpass filters 84 a, 84 b, 84 c, and 84d, and then digitized using respective A/D converters 86 a, 86 b, 86 c,and 86 d, for respectively providing a 0° phase shifted demodulateddigital signal, a 90° phase shifted demodulated digital signal, a 135°phase shifted demodulated digital signal, and a 225° phase shifteddemodulated digital signal. The outputs of the downconverter mixers 76a, 76 b, 76 c, and 76 d are representations of the components of thefour LPE signals. The 0° downconverter mixer 76 a will produce theinphase component p_(m1)(n), and the 90° downconverter mixer 76 b willproduce the quadrature component q_(m1)(n). Likewise, the downconvertermixers 76 c and 76 d will produce the same output, that is, the 135°downconverter mixer 76 c will provide an inphase component p_(m2)(n) andthe 225° downconverter mixer 76 d will produce the quadrature componentq_(m2)(n), both rotated by 135°. In terms of p_(m1)(n) and q_(m1)(n),the output of the second downconverter pair 76 c and 76 d may beexpressed as {tilde over(x)}_(m2)(n)=−(1/√2)[p_(m1)(n)+q_(m1)(n)]+(j/√2)[p_(m1)(n)−q_(m1)(n)],where p_(m1)(n) is the inphase component and q_(m1)(n) is the quadraturecomponent of the received signal {tilde over (x)}_(m1)(n). The outputsof the A/D converters 86 a, 86 b, 86 c, and 86 d are digitized versionsof the downconverter mixer outputs. These four phase shifted demodulateddigital signals are communicated to a signal processor 88 for removingerrors and imbalances during splitting and downconverting, as shown bydashed lines for QPSK in FIG. 6 having D constellation points as opposedto an ideal constellation having P constellation points.

The purpose of the signal processor 88 is to remove or minimize errorsand imbalances generated during splitting and downconverting of thereceived signal by application of analytical techniques. The 0° phaseshifted demodulated digital signal and the 90° phase shifted demodulateddigital signal for a first pair of downconverted digital signals, andthe 135° phase shifted demodulated digital signal and the 225° phaseshifted demodulated digital signal for a second pair of downconverteddigital signals. The signal processor 88 can be an application specificintegrated circuit (ASIC), a field programmable gate array (FPGA), or amicrocomputer executing software for implementing signal processingfunctions 90 a, 90 b, 92, and 94 and conventional hardware forimplementing signal conversion. The signal processor 88 computes alowpass equivalence (LPE) {tilde over (x)}_(m1) for the first pair ofdigital signals of the first I and Q downconverter pair 76 a and 76 b,and, computes a LPE {tilde over (x)}_(m2) for the second pair of digitalsignals of the second I and Q downconverter pair 76 c and 76 d.

Once the four downconverted signals are in digital form, digitalprocessing can be applied. Specifically, the first pair of digitalsignals can be digitally combined to form the LPE signal represented{tilde over (x)}_(m1) as a first measurement, and the second pair ofdigital signals can be digitally combined to form the LPE signalrepresented {tilde over (x)}_(m2) as a second measurement, by LPEcalculate functions 90 a and 90 b. Then, the first and second LPEmeasurement {tilde over (x)}_(m1) and {tilde over (x)}_(m2) are alignedin phase using an alignment in phase and time and averaging function 92for providing a balanced LPE signal {tilde over (x)}_(ma). These signalprocessing functions are closed-form computations that can beimplemented in an ASIC, FPGA, or microcomputer. The result of the signalprocessing steps 90 a, 90 b, and 92 is an LPE signal that isautomatically corrected for amplitude and phase imbalances in thedownconverters mixers 76 a, 76 b, 76 c, and 76 d, and splitters 80, 82a, 82 b, 63, 64, and 66. The balanced LPE {tilde over (x)}_(ma) signalcan then be converted into real form by conventional complex to realsignal conversion for providing I and Q baseband signals that aredigital signals that can then be demodulated using an I and Q basebanddata demodulator 96 that provides an output data stream 98.

Referring to all of the figures, the removal of imbalances on thereceived signal in the enhanced receiver system can be modeled. Waveformmeasurement error and imbalances are conveniently defined in terms of anormalized mean square error metric (NMSE). The NMSE metric is used todetermine quantitatively the distance between two waveforms. It is twotimes the sum over all sample points of the square of the voltagedifference between the two waveforms divided by the sum over all samplepoints of the square of the voltages in both waveforms, which isminimized with respect to phase and time. Equivalently, this may beexpressed as the total error power between the two waveforms divided bythe arithmetic average of the power in the two waveforms. The NMSE iscalculated from the complex, LPE waveforms {tilde over (x)}_(m1) and{tilde over (x)}_(m2) in an NMSE equation.

${{NMSE}( {{\overset{\sim}{x}}_{m\; 1},{\overset{\sim}{x}}_{m\; 2}} )} = {\min_{\varphi,k}\lbrack {2\frac{\sum\limits_{n}{{{{{\overset{\sim}{x}}_{m\; 1}( {n + k} )}{\mathbb{e}}^{- {j\varphi}}} - {{\overset{\sim}{x}}_{m\; 2}(n)}}}^{2}}{{\sum\limits_{n}{{{\overset{\sim}{x}}_{m\; 1}(n)}}^{2}} + {\sum\limits_{n}{{{\overset{\sim}{x}}_{m\; 2}(n)}}^{2}}}} \rbrack}$

The NMSE for LPE waveforms is minimized with respect to phase φ and timeindex k by aligning the waveforms in time and in the complex plane. AnNMSE algorithm used for repetitive waveforms is a complex circularcross-correlation function. In this circular cross correlation, thewaveforms are rotated relative to each other. The maximum value of thecross-correlation algorithm indicates proper phase and time alignment ofthe two waveforms. To obtain fine time resolution, the waveforms areunsampled by a factor of ten or more over hardware sampling, usinglinear or sinc interpolation, to obtain finer time resolution. Analternative, frequency domain algorithm may be used. Thefrequency-domain algorithm is faster than the time-domain algorithmbecause upsampling is not required.

The phase shift error analysis proceeds from an LPE signalrepresentation equation {tilde over (x)}(n)=p(n)+jq(n). The receivedsignal {tilde over (x)}(n) has an inphase component p(n), and aquadrature component q(n). One point of this waveform is shown in vectorform in the complex plane in FIG. 5. The I and the Q axes are π/2 apart.However, in a measurement, the axes may deviate from π/2 by a smalltotal LO phase shifter setting error 2δ₁. This total error may besymmetrically distributed between the I and Q components to simplify thefollowing error analysis. The LO phase shift between the I and Qcomponents using sampling is (π/2)−2δ₁, where the phase shifter settingerror, δ₁<<1. Using this assumption, the measured waveform is defined byan {tilde over (x)}_(m1) first measurement equation.{tilde over (x)} _(m1)(n)=p _(m1)(n)+jq _(m1)(n)=p(n)+δ₁ q(n)+j[q(n)+δ₁p(n)]

If the measurement or sampling is repeated, and the error δ₁ is the samefor both measurements, with δ₁=δ₂, the two waveforms will agreeperfectly to within a bound set by the measurement system noise level.Both measurements are in error compared to the actual waveform, but theerror cannot be determined. However, the invariance of the signal withrespect to the absolute value of the LO phase allows detection of theerror caused by δ₁. The second measurement is taken after inserting anabsolute LO phase shift θ, by means of the second phase shifter. Topreserve the generality of the analysis, the second measurement isassumed to have a different angular error of δ₂ instead of δ₁. Thesecond measurement is then given by an {tilde over (x)}_(m2) secondmeasurement equation with δ₂<<1.

${{\overset{\sim}{x}}_{m\; 2}(n)} = {{{p(n)}\cos\;\theta} + {{q(n)}\sin\;\theta} + {{q(n)}\delta_{2}\cos\;\theta} - {{p(n)}\delta_{2}\sin\;\theta} + {j\lbrack {{{q(n)}\cos\;\theta} - {{p(n)}\sin\;\theta} + {{p(n)}\delta_{2}\cos\;\theta} + {{q(n)}\delta_{2}\sin\;\theta}} \rbrack}}$

First and second measurements can be compared by means of the NMSEequation. As shown in FIG. 5, the signal vectors are plotted in an I andQ complex coordinate system. Measurement axes are skewed by the errorangle δ₁ and the projections along these I and Q axes can be measured.The ideal signal vector is p(n)+jq(n) while the measured signal isp_(m1)(n)+jq_(m1)(n). However, as in the NMSE equation, {tilde over(x)}_(m1)(n) must be rotated analytically by an angle φ to line it upwith measurement {tilde over (x)}_(m2)(n) using a rotated measurementequation.

${{\overset{\sim}{x}}_{m\; 1}{\mathbb{e}}^{{- j}\;\varphi}} = {{{p(n)}\cos\;\varphi} + {{q(n)}\delta_{1}\cos\;\varphi} + {{q(n)}\sin\;\varphi} + {{p(n)}\delta_{1}\sin\;\varphi} + {j\lbrack {{{q(n)}\cos\;\varphi} + {{p(n)}\delta_{1}\cos\;\varphi} - {{p(n)}\sin\;\varphi} - {{q(n)}\delta_{1}\sin\;\varphi}} \rbrack}}$

The NMSE between {tilde over (x)}_(m1)(n) and {tilde over (x)}_(m2)(n),where the time alignment between the two measured waveforms has alreadybeen performed, is defined by a difference NMSE equation.

${{NMSE}( {{\overset{\sim}{x}}_{m\; 1},{\overset{\sim}{x}}_{m\; 2}} )} = {\min\limits_{\phi}\lbrack {2\frac{\sum\limits_{n}{{{{{\overset{\sim}{x}}_{m\; 1}(n)}{\mathbb{e}}^{- {j\varphi}}} - {{\overset{\sim}{x}}_{m\; 2}(n)}}}^{2}}{{\sum\limits_{n}{{{\overset{\sim}{x}}_{m\; 1}(n)}}^{2}} + {\sum\limits_{n}{{{\overset{\sim}{x}}_{m\; 2}(n)}}^{2}}}} \rbrack}$

From the first and second measurement equations and the difference NMSEequation, and minimizing with respect to phase φ, an alignment and phaseequation provides an expression for φ.

$\varphi = {- {\tan^{- 1}\lbrack \frac{\begin{matrix}{{( {{\delta_{1}\delta_{2}} - 1} )\sin\;\theta{\sum\limits_{n}\lbrack {{p(n)}^{2} + {q(n)}^{2}} \rbrack}} +} \\{( {\delta_{2} - \delta_{1}} ){\sum\limits_{n}\lbrack {{( {{p(n)}^{2} - {q(n)}^{2}} )\cos\;\theta} + {2{p(n)}{q(n)}\sin\;\theta}} \rbrack}}\end{matrix}}{\begin{matrix}{{( {{\delta_{1}\delta_{2}} + 1} )\cos\;\theta\;{\sum\limits_{n}\lbrack {{p(n)}^{2} + {q(n)}^{2}} \rbrack}} +} \\{( {\delta_{2} + \delta_{1}} ){\sum\limits_{n}\lbrack {{( {{q(n)}^{2} - {p(n)}^{2}} )\sin\;\theta} + {2{p(n)}{q(n)}\cos\;\theta}} \rbrack}}\end{matrix}} \rbrack}}$

The communication signals analyzed can be approximated with anapproximate rotation of φ=θ, by assuming a four quadrant equation.

${{\sum\limits_{n}\lbrack {{q(n)}^{2} - {p(n)}^{2}} \rbrack}}\mspace{11mu}{\operatorname{<<}\;{\sum\limits_{n}{q(n)}^{2}}}$

The approximation also assumes a negligible DC component equation.

$\sum\limits_{n}\;{{p(n)}{q(n)}{\operatorname{<<}{\sum\limits_{n}\;{p(n)}^{2}}}}$

The four quadrant equation and negligible DC component equation appliesto waveforms having 4-fold rotational symmetry, for example, QPSK and16-QAM. The approximation of the negligible DC component equationapplies to baseband waveforms having a power in the DC component smallcompared to the total power. This applies to most amplitude andphase-shift keyed waveforms, but not AM, for example. Assumptions of thefour quadrant equation and the negligible DC component equation isapplied to subsequent NMSE calculations. Applying the four quadrant andthe negligible DC component equations to the alignment and phaseequation provide that φ=θ. In practice, the software algorithm providesthe optimum value of φ from the two measured waveforms, thus determiningthe experimentally unknown value of θ for providing an expanded NMSEequation.

${{NMSE}( {{\overset{\sim}{x}}_{m\; 1},{\overset{\sim}{x}}_{m\; 2}} )} = {\sum\limits_{n}\;\frac{\begin{Bmatrix}{\lbrack {{{q(n)}\delta_{1}\cos\;\theta} + {{p(n)}\delta_{1}\sin\;\theta} - {{q(n)}\delta_{2}\cos\;\theta} + {{p(n)}\delta_{2}\sin\;\theta}} \rbrack^{2} +} \\\lbrack {{{p(n)}\delta_{1}\cos\;\theta} - {{q(n)}\delta_{1}\sin\;\theta} - {{p(n)}\delta_{2}\cos\;\theta} - {{q(n)}\delta_{2}\sin\;\theta}} \rbrack^{2}\end{Bmatrix}}{2{p(n)}^{2}}}$

The expanded NMSE equation can be simplified from the four quadrantequation and the negligible DC component equation into an NMSE phaseerror equation.NMSE({tilde over (x)} _(m1) ,{tilde over (x)} _(m2))=δ₁ ²+δ₂ ²−2δ₁δ₂ cos2θ

From the NMSE phase error equation, some phase shifter setting errorswill not be detectable for certain values of θ. For example, ifθ=π/2+mπ, where m is an integer, and δ₁=−δ₂, the calculated NMSE wouldbe zero even though δ₁ and δ₂ are nonzero. Similarly, if θ=mπ, andδ₁=δ₂, the calculated NMSE would also be zero even though δ₁ and δ₂ arenonzero. To determine the optimum value θ for use in detecting andcorrecting phase shifter setting errors, the error between the measuredwaveforms and the actual waveform are analyzed. Substituting the firstwaveform equation and into the NMSE equation yields the NMSE between thefirst measured waveform and the actual waveform providing a first actualphase error equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{m\; 1}} )} = {{\sum\limits_{n}\;\frac{\lbrack {{q(n)}\delta_{1}} \rbrack^{2} + \lbrack {{p(n)}\delta_{1}} \rbrack^{2}}{2{p(n)}^{2}}} = \delta_{1}^{2}}$

Similarly, substituting the second waveform equation into the NMSEequation yields the NMSE between the second measured waveform and theactual waveform providing a second actual phase error equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{m\; 2}} )} = {{\sum\limits_{n}\;\frac{\lbrack {{q(n)}\delta_{2}} \rbrack^{2} + \lbrack {{p(n)}\delta_{2}} \rbrack^{2}}{2{p(n)}^{2}}} = \delta_{2}^{2}}$

The first and second actual phase error equations describe the error inthe first and second measurements, respectively. An NMSE softwarealgorithm can be used to phase align the two measured waveforms. Optimalphase alignment between the two measured waveforms is achieved when theNMSE is minimized. The phase-aligned waveforms may be averaged to yielda prediction of the actual waveform using an actual average waveformequation.

$\begin{matrix}{{\overset{\sim}{x}}_{ma} = {\frac{1}{2}( {{{\overset{\sim}{x}}_{m\; 1}{\mathbb{e}}^{{- j}\;\theta}} + {\overset{\sim}{x}}_{m\; 2}} )}} \\{= {{{p(n)}\cos\;\theta} + {{q(n)}\sin\;\theta} + {\frac{1}{2}{q(n)}\delta_{1}\cos\;\theta} + {\frac{1}{2}{p(n)}\delta_{1}\sin\;\theta} +}} \\{{\frac{1}{2}{q(n)}\delta_{2}\cos\;\theta} - {\frac{1}{2}{p(n)}\delta_{2}\sin\;\theta} +} \\{j\lbrack {{{q(n)}\cos\;\theta} - {{p(n)}\sin\;\theta} + {\frac{1}{2}{p(n)}\delta_{1}\cos\;\theta} - {\frac{1}{2}{q(n)}\delta_{1}\sin\;\theta} +} } \\ {{\frac{1}{2}{p(n)}\delta_{2}\cos\;\theta} + {\frac{1}{2}{q(n)}\delta_{2}\sin\;\theta}} \rbrack\end{matrix}$

Calculating the NMSE between this average waveform and the actualwaveform yields an actual average phase error NMSE equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{ma}} )} = {\frac{1}{4}{\sum\limits_{n}\;\frac{\begin{Bmatrix}{\lbrack {{{q(n)}\delta_{1}\cos\;\theta} + {{p(n)}\delta_{1}\sin\;\theta} + {{q(n)}\delta_{2}\cos\;\theta} - {{p(n)}\delta_{2}\sin\;\theta}} \rbrack^{2} +} \\\lbrack {{{p(n)}\delta_{1}\cos\;\theta} - {{q(n)}\delta_{1}\sin\;\theta} + {{p(n)}\delta_{2}\cos\;\theta} + {{q(n)}\delta_{2}\sin\;\theta}} \rbrack^{2}\end{Bmatrix}}{2{p(n)}^{2}}}}$

The actual average phase error NMSE equation can be simplified into asimplified actual average phase error NMSE equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{ma}} )} = {\frac{1}{4}\lbrack {\delta_{1}^{2} + \delta_{2}^{2} + {2\delta_{1}\delta_{2}\cos\; 2\theta}} \rbrack}$

The average waveform has 3.0 dB lower thermal noise than either first orsecond measurements alone. The actual waveform is not measurable, hencethe NMSE for the actual average phase error NMSE equation cannot becalculated from measurements. However the NMSE between the two measuredwaveforms is easily calculated. The NMSE between the two measuredwaveforms may be compared to the error in the average waveform.Comparison of NMSE phase error equation and simplified actual averagephase error NMSE equation allow the range of θ to be calculated suchthat the NMSE between the two measured waveforms is greater than theerror in the average waveform for all values of δ₁ and δ₂. This range ofθ is given by a rotational phase limit equation.

${{\frac{1}{2}{\cos^{- 1}( \frac{3}{5} )}} + \frac{m\;\pi}{2}} < \theta < {{( {m + 1} )\frac{\pi}{2}} - {\frac{1}{2}{\cos^{- 1}( \frac{3}{5} )}}}$

In the rotational phase limit equation, m is an integer and the NMSEbetween the two waveform measurements is greater than the error in theaverage waveform for all values of δ₁ and δ₂. A practical choice of θfor measurements is the middle of the region defined by rotational phaselimit equation with θ_(OPT)=π/4+mπ/2. For these values of θ, NMSE({tildeover (x)}_(m1),{tilde over (x)}_(m2))/4=NMSE({tilde over (x)},{tildeover (x)}_(ma)). For θ_(OPT), the error of the average waveform is 6.0dB lower than the NMSE between the two measurements. Hence, theθ_(OPT)=π/4+mπ/2 for removing phase imbalances.

Imbalances also occur for LO amplitude variations. Consider an LPEsignal represented by {tilde over (x)}(n)=p(n)+jq(n). When the LO powerlevel is different between the inphase and quadrature measurement, theoverall gain of the downconverting receiver will be different betweenthe two measurements. There is no loss in generality by normalizing thecomplex signal amplitude. Hence, the error may be symmetricallydistributed between the I and Q components to simplify error analysis.

The gain for the inphase measurement is 1+ε₁ and the gain for thequadrature component is 1−ε₁, the first measurement is defined by afirst amplitude equation.{tilde over (x)} _(m1)(n)=p _(m1)(n)+jq_(m1)(n)=p(n)(1+ε₁)+j[q(n)(1−ε₁)]

A second measurement is performed after rotation by θ, with am amplitudeimbalance ε₂, for providing a second amplitude equation.{tilde over (x)} _(m2)(n)=(1+ε₂)[p(n) cos θ+q(n) sin θ]+j{(1−ε₂)[q(n)cos θ−p(n) sin θ]}

The first and second measurements can again be compared by the NMSEequation. However, {tilde over (x)}_(m1)(n) must be rotated analyticallyby an angle φ to line the first measurement with the second measurementwith the rotation defined by a rotated amplitude equation.

${{\overset{\sim}{x}}_{m\; 1}{\mathbb{e}}^{{- j}\;\varphi}} = {{( {1 + ɛ_{1}} ){p(n)}\cos\;\varphi} + {( {1 - ɛ_{1}} ){q(n)}\sin\;\varphi} + {j\lbrack {{( {1 - ɛ_{1}} ){q(n)}\cos\;\varphi} - {( {1 + ɛ_{1}} ){p(n)}\sin\;\varphi}} \rbrack}}$

Using the second amplitude equation, the rotated amplitude equation, thedifference NMSE equation first, the approximations of the four quadrantand negligible DC component equations, with ε₁, ε₂<<1, φ=θ, forproviding an NMSE amplitude error equation.NMSE({tilde over (x)} _(m1) ,{tilde over (x)} _(m2))=ε₁ ²+ε₂ ²−2ε₁ε₂ cos2θ

Hence, the amplitude error in the first measured waveform can becalculated using a first NMSE amplitude error equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{m\; 1}} )} = {{\sum\limits_{n}\;\frac{\lbrack {{q(n)}ɛ_{1}} \rbrack^{2} + \lbrack {{p(n)}ɛ_{1}} \rbrack^{2}}{2{p(n)}^{2}}} = ɛ_{1}^{2}}$

Similarly, the error in the second measured waveform can be calculatedusing a second NMSE amplitude error equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{m\; 2}} )} = {{\sum\limits_{n}\;\frac{\lbrack {{q(n)}ɛ_{2}} \rbrack^{2} + \lbrack {{p(n)}ɛ_{2}} \rbrack^{2}}{2{p(n)}^{2}}} = ɛ_{2}^{2}}$

From the first and second amplitude error equation, the error in theaverage waveform is defined by an average NMSE amplitude error equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{ma}} )} = {\frac{1}{4}\lbrack {ɛ_{1}^{2} + ɛ_{2}^{2} + {2ɛ_{1}ɛ_{2}\cos\; 2\theta}} \rbrack}$

Because of the similarity of the analysis, the optimal value of θremains θ_(OPT) for both phase and amplitude error calculations. The useof θ_(OPT) for waveform measurements has the further advantage that itenables automatic detection of nonlinearities occurring after thedownconversion, including baseband amplifier nonlinearities and A/Dnon-ideality. The system can be used for baseband nonlinearitydetection. The first measurement without imbalances would be is definedby {tilde over (x)}_(m1)(n)=p(n)+jq(n) while the second measurement isdefined by {tilde over (x)}_(m2)(n)=p(n)cos θ+q(n)sin θ+j[q(n)cosθ−p(n)sin θ]. However, baseband nonlinearities will not be detectablefor certain values of θ. For example, if θ=mπ/2, the original inphaseand quadrature components (p,q) are transformed to either (p,q), (−q,p),(q,−p), or (−p,−q). In the process of calculating the NMSE, all thesepossibilities are transformed back to the original components, (p,q).Therefore, the NMSE between the two measurements would be zero even inthe presence of baseband nonlinear distortion, assuming the nonlinearityis symmetric about zero voltage. However, the use of θ_(OPT) causes p(n)and q(n) to be mixed between the two measurements. For the secondmeasurement, the inphase and quadrature components both contain equalmagnitudes of p(n) and q(n). For a communications signal, p(n) and q(n)are uncorrelated quantities because they carry independent information.Mixing of p(n) and q(n) in equal magnitudes causes different basebandnonlinear distortions in the second measurement compared to the firstmeasurement. The NMSE between the first and second measurements willprovide a quantitative assessment of the nonlinearity.

By the minimization of the NMSE between the first and secondmeasurements, the system may be optimized to reduce nonlinearities inthe presence of noise. For analog components, lowering the signal levelusually reduces the nonlinear error. For A/Ds, the signal level must beincreased when the quantization error is dominant, or reduced if thedominant effect is waveform clipping when the signal exceeds the A/Drange. The NMSE also includes thermal noise, which may be minimized byhigher signal level or increased waveform averaging.

With θ=3π/4 in waveform measurements, the overall error in the averagewaveform caused by both amplitude and phase imbalance is defined by anaverage actual NMSE amplitude and phase equation.

${{NMSE}( {\overset{\sim}{x},{\overset{\sim}{x}}_{ma}} )} = {\frac{1}{4}\lbrack {ɛ_{1}^{2} + ɛ_{2}^{2} + \delta_{1}^{2} + \delta_{2}^{2}} \rbrack}$

With θ=3π/4, the NMSE between the first and second measurements causedby both amplitude and phase imbalance is defined by measured NMSEamplitude and phase equation.NMSE({tilde over (x)}_(m1),{tilde over (x)}_(m2))=ε₁ ²+ε₂ ²+δ₁ ²+δ₂ ²

An NMSE between the two measured waveforms is less than −50 dB. Theerror in the averaged waveform is therefore less than −56 dB. The I/Qgain imbalance is less than 0.04 dB with a phase imbalance of less than0.25 degrees. Such a small phase imbalance is achieved by adjusting thephase shifter to minimize NMSE. Gain imbalance is not easily adjusted,however, the mixer is used at an LO power that yields near minimumconversion loss. Hence, conversion loss is insensitive to variations inLO power. The LO power imbalance in dB between the two phase settingscauses a much smaller I/Q gain imbalance in dB.

Measurement of the signal component at the LO frequency occurs with theuse θ=3π/4 with four waveform measurements taken at the phases 0, andπ/2, that is 0° and 90° for the first measurement and 3π/4, and 5π/4,that is, 135° and 225° for the second measurement.

The complete measurement system not only requires measurement of thewaveforms, but a separate measurement of the component at the LOfrequency. This is accomplished by means of the voltmeter. At each ofthe phases, the voltage at the mixer I port is recorded using thevoltmeter. These four voltage measurements, along with voltagemeasurements at the four phase settings with zero signal level applied,can be used to extract the signal component at the LO frequency at 0,π/2, 3π/4, and 5π/4 phase shifts.

The receiver can use a continuously variable waveguide phase shifterthat may be calibrated at any operating frequency within the specifiedwaveguide band such as between 18 GHz to 26.5 GHz. A second receiverimplementation uses a fixed-tuned, switched-coaxial-line phase shifterthat has the advantage of shorter measurement time, but only operates ata fixed local oscillator frequency.

The continuously variable phase shifter can be implemented in a K-bandwaveguide, and is computer controlled. The continuously variable phaseshifter utilizes a waveguide circulator and a waveguide non-contactingchoke-type adjustable short security. The carrier signal enters thewaveguide, reflects off the dumbbell short connected, and exits thecirculator that is attached to the L port of the mixer. The axialposition of the dumbbell short within the waveguide is changed by meansof model 850G-HS motorized linear actuator manufactured by NewportCorporation. The actuator has 50 mm travel range with 2.0 μmbidirectional repeatability. This corresponds to a range of over 1000°at 18.0 GHz, and a repeatability of 0.04° at 22.0 GHz. The variation inloss through the phase shifter as a function of short position isapproximately 0.3 dB, and is caused by VSWR effects. This results in avariation in LO drive to the downconverting mixer, and causes minorerrors in the measurement by slight variations in rf to basebandconversion loss at each of the LO phase settings used. This variation inloss is minimized by setting the LO drive into the mixer at a powerlevel where the conversion loss is a minimum.

An optimization process is used to calibrate the phase shifter. Usingstarting values of the phase shifter positions derived from networkanalyzer measurements, communications signal waveforms are captured andthe NMSE, and LO phase shift θ are calculated. The phase shifterpositions are then varied with waveform measurements done after eachvariation, with the goal of attaining the lowest value of NMSE, andobtaining θ=135°. In practice, an NMSE of better than −40 dB can beachieved, and with a value for θ in the range of 135±0.5°. When thesevalues are achieved, the four phase shifter positions will be 0°, 90°,135°, and 225°.

The second fixed-tuned phase shifter implementation uses coaxialmicrowave switches to switch different line lengths in and out of the LOpath. For this phase shifter to achieve good performance, the lossthrough all the line lengths must be well matched, and the differentialelectrical length through the various paths must be stable overtemperature and time, and relatively immune to shock and vibration. With20 GHz carrier and using commercial SMA and 3.5 mm coaxial components,the switches used were HP 8765C single-pole, double throw, latchingtype, connected by means of SMA male barrels, SMA swept radius 90°elbows, and SMA airline phase trimmers. These switches were chosenbecause they could be operated by means of a 30.0 ms current pulse toeffect the switching. This switching eliminates power dissipation andheating of the tuned line lengths, which has been seen to causesignificantly phase shifter setting errors. The phase trimmers were setapproximately using a network analyzer, then the values were optimizedin the same manner as the waveguide phase shifter. The variation in lossbetween the various paths was less than ±0.3 dB, and the accuracy of thephase shift values was as good as the waveguide phase shifter. Thiscoaxial phase shifter is easier to construct and is faster in operationthan the waveguide phase shifter. The main disadvantage of the coaxialdesign is that the line lengths are difficult to change, making itcumbersome to use when measured waveforms at different LO frequenciesare needed.

As an example of the kinds of measurements that can be performed, andthe accuracy that can be achieved, a quadrature-phase-shift-key (QPSK)waveform at a carrier frequency of 20.7 GHz and a symbol rate of 40Megasymbols/second was measured. A 127-symbol sequence was measured,corresponding to a total time duration of the waveform of 3.172 μs. Toshow the errors more dramatically, a measurement can be performed wherethe continuously variable waveguide phase shifter was set intentionallyto incorrect values. The phase shifter values were set at approximately0°, 75°, 135°, and 210° and for a second error test the values were setto 0°, 75°, 120°, and 225°. For both error tests the two waveformmeasurements {tilde over (x)}_(m1) and {tilde over (x)}_(m2) wererotated in software for best alignment with the actual best waveformmeasurement where the phase shifter valves are set to 0°, 90°, 135°, and225°. The calculated NMSE between any two measurements is approximately−24 dB. The averaged measurements {tilde over (x)}_(ma) show theadvantage of averaging. The NMSE of the averaged waveform with the bestwaveform is −33 dB, while the NMSE of the any of the four skewedwaveforms with the best waveform measurement was approximately −27 dB.

The accuracy of baseband complex signal measurements or the removal ofimbalances in receiver systems has been improved. Two sets of inphaseand quadrature waveforms are recorded. The first set using LO phaseshifts of 0 and π/2, the second set using LO phase shifts of θ andπ/2+θ. The normalized mean square error (NMSE) between the twomeasurements is a sensitive indication of I and Q phase and amplitudeimbalance and baseband nonlinearities. Using θ=π/4+mπ/2, phase andamplitude imbalances of any sign and magnitude cause NMSE errors.Averaging the two measurements for these values of θ yields ameasurement error 6.0 dB less than the NMSE between the twomeasurements. Because the NMSE can be determined for each set of twosignal measurements, the measurement system may be adjusted to minimizeI and Q imbalances and nonlinearities. Such adjustments enable the errorcaused by I and Q imbalances to be consistently below −56 dB. Thisaccuracy is useful for communications system modeling efforts andreceiver implementations.

The system can be applied to the calibration of any direct demodulationreceiver. The receiver I and Q downconverter may be connected to awaveform recording instrument to measure a repetitive complex basebandsignal twice, with a rotation of LO phase performed between the twomeasurements, and then compare the two measurements by means of NMSE.This provides a sensitive indicator of receiver I and Q imbalances andnonlinearities. The system can be applied to test systems as well ascommunication systems for reducing downconverter imbalances. Thoseskilled in the art can make enhancements, improvements, andmodifications to the invention, and these enhancements, improvements,and modifications may nonetheless fall within the spirit and scope ofthe following claims.

1. A method for at least one of removing and minimizing errors andimbalances generated during splitting and downconverting of a receivedsignal, comprising: computing a lowpass equivalence (LPE) for a firstpair of digital signals from a first I and Q downconverter pair;computing a LPE for a second pair of digital signals of a second I and Qdownconverter pair; combining the first pair of digital signals to formthe LPE signal representing a first LPE measurement, and combining thesecond pair of digital signals to form the LPE signal representing asecond LPE measurement; aligning the first and second LPE measurement inphase using alignment, time and averaging function for providing abalanced LPE signal; and generating I and Q baseband signals byconverting the balanced LPE signal into real form by complex to realsignal conversion.
 2. A method for determining lowpass equivalencies(LPE) of generated baseband signals, comprising: providing a localcarrier and phase shifter means for phase shifting the local carrier byphase shifts to provide phase shifted carriers, wherein the phase shiftsare 0°, 90°, θ and θ+π/2 and θ=π/4+mπ/2 where m is an integer;downconverting an input signal into the generated baseband signals,wherein the input signal having a carrier modulated by an input basebandsignal, the phase shifted carriers being phase shifted replicas of thecarrier, and providing processor means for receiving the generatedbaseband signals and for determining the lowpass equivalencies of thegenerated baseband signals.
 3. The method of claim 2 wherein, theprocessor means is further for determining signal imbalances in thegenerated baseband signals created during downconversion of the inputsignal by the downconverter means.
 4. The method of claim 2 wherein, theprocessor means is further for determining signal imbalances in thegenerated baseband signals created during downconversion of the inputsignal by the downconverter means, and the signal imbalances consistingof phase and amplitude signal imbalances.
 5. The method of claim 2wherein, the processor means is further for determining signalimbalances in the generated baseband signals created duringdownconversion of the input signal by the downconverter means, theprocessor means is further for removing the signal imbalances from thebaseband signals, and the signal imbalances consisting of phase andamplitude signal imbalances.
 6. The method of claim 2 wherein, theprocessor means is further for removing the signal imbalances from thebaseband signals, and the processor means computes lowpass equivalenciesof the generated baseband signals, aligns the lowpass equivalencies inphase and time, and averages the aligned lowpass equivalencies into anaverage baseband signal being a replica of the input baseband signal. 7.The method of claim 2 wherein, the input signal is a quadrature signalhaving an inphase component and a quadrature component, and thegenerated baseband signals are inphase generated baseband signals andquadrature generated baseband signals.
 8. The method of claim 2, whereinthe input signal is a quadrature signal having an inphase component anda quadrature component, the generated baseband signals are first andsecond generated inphase baseband signals and first and second generatedquadrature baseband signals, and the lowpass equivalencies being a firstlowpass equivalence of the first generated inphase baseband signal andthe first generated quadrature baseband signal and being a secondlowpass equivalence of the second generated inphase baseband signal andthe second generated quadrature baseband signal.
 9. The method of claim2, wherein the input, signal is a quadrature signal having an inphasecomponent and a quadrature component, the generated baseband signals arefirst and second generated inphase baseband signals and first and secondgenerated quadrature baseband signals, and the lowpass equivalenciesbeing a first lowpass equivalence of the first generated inphasebaseband signal generated using the 0° phase shift, and the firstgenerated quadrature baseband signal using the 90° phase shift and beinga second lowpass equivalence of the second generated inphase basebandsignal generated using the .theta. phase shift and the second generatedquadrature baseband signal generated using the θ+π/2 phase shift. 10.The method of claim 2, wherein m equals 1 and the phase shifts are 0°,90°, 135°, and 225°.
 11. The method of claim 2, further comprising:removing the signal imbalances from the generated baseband signals; andgenerating a replica baseband signal of the input baseband signal. 12.The method of claim 2, further comprises: removing the signal imbalancesfrom the generated baseband signals, and the processor means is furtherfor generating a replica baseband signal from the generated basebandsignals, the replica baseband signal being a replica of the inputbaseband signal.